Local rigidity of discrete groups acting on complex hyperbolic space

1987 ◽  
Vol 88 (3) ◽  
pp. 495-520 ◽  
Author(s):  
W. M. Goldman ◽  
J. J. Millson
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Discrete Groups ◽  
Local Rigidity

scholarly journals Bounded cohomology and totally real subspaces in complex hyperbolic geometry

2011 ◽  
Vol 32 (2) ◽  
pp. 467-478 ◽  
Author(s):  
MARC BURGER ◽  
ALESSANDRA IOZZI
Keyword(s):  
Hyperbolic Space ◽  
Hyperbolic Geometry ◽  
Isometry Group ◽  
Complex Hyperbolic Space ◽  
Discrete Groups ◽  
Connected Component ◽  
Bounded Cohomology ◽  
Finitely Generated ◽  
Complex Hyperbolic Geometry ◽  
Totally Real

AbstractWe characterize representations of finitely generated discrete groups into (the connected component of) the isometry group of a complex hyperbolic space via the pullback of the bounded Kähler class.

SHIMIZU’S LEMMA FOR COMPLEX HYPERBOLIC SPACE

1992 ◽  
Vol 03 (02) ◽  
pp. 291-308 ◽  
Author(s):  
JOHN R. PARKER
Keyword(s):  
Hyperbolic Space ◽  
Hyperbolic Plane ◽  
Discrete Group ◽  
Complex Hyperbolic Space ◽  
Necessary Condition ◽  
Higher Dimensional ◽  
Group Of Isometries ◽  
Vertical Translation

Shimizu’s lemma gives a necessary condition for a discrete group of isometries of the hyperbolic plane containing a parabolic map to be discrete. Viewing the hyperbolic plane as complex hyperbolic 1-space we generalise Shimizu’s lemma to higher dimensional complex hyperbolic space In particular we give a version of Shimizu’s lemma for subgroups of PU (n, 1) containing a vertical translation Partial generalisation to groups containing either an ellipto-parabolic map or non-vertical translations are also given together with examples that show full generalisation is not possible in these cases

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